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Also known as 'total alkalinity' or 'acid-neutralizing capacity' (ANC) in some countries.

The ‘K’ in KH comes from the German word 'karbonate'. KH is a measure of bicarbonate (HCO3-) and carbonate (CO32-) ions that act as buffers in the water to prevent the pH dropping or changing sharply (especially at night if you have plants in the aquarium).
One degree KH is equal to 17.9 mg/I (ppm) CaCO3. It's also measured in degrees. The degree symbol may be replaced with a d (ie. 2 dKH).

A common misconception is that KH is a part of GH and that KH cannot be higher than GH. There is no such correlation. In some areas, the water contains more sodium bicarbonate and/or potassium bicarbonate than total calcium and magnesium. In these areas, the KH is naturally higher than the GH. Furthermore, people using water softeners will most likely have a KH that is higher than the GH, as water softeners exchange sodium or potassium ions for calcium, magnesium, and other hard water minerals.

In tanks with a low KH value, say under 2-3d (35.7-53.6ppm), pH crash is more likely.

KH is consumed by nitrifying bacteria 24/7 so either your substrate generates more, you perform water changes to supplement it or you add chemicals to add KH to your aquarium as otherwise it causes a pH crash/shock.

Tip: get up just before the tank lights (or sun light) come on and measure the pH and observe the animals for stress. It may be substantially different than it is during the middle of the day.

Sodium bicarbonate (NaHCO3) (baking soda/bicarbonate of soda) is the usual KH additive of choice. It's cheap and easy to find and use. It will however raise pH because the added bicarbonate will serve as a buffer to bind hydrogen ions (protons). The increase in pH is limited and usually not a concern because the carbonic acid formed dissociates to CO2 and water.

Potassium bicarbonate (KHCO3) is another KH additive. It's cheap. But not so easy to find, it's a specialist food additive for people who don't want sodium in their food. It will however raise pH for the same reason just described. It dissolves much faster than the Potassium or Calcium carbonate powders.